In our discussion of the dummy variables for schooling levels of table 14.4, we assert that the substantive results of a regression are the same, regardless of which dummy variable we omit. Table 14.10 presents the pooled regression of table 14.4 with a single substitution. We include the dummy variable for those with no schooling, but omit that for the few with doctorate degrees.

(a) How do the Râ•›2, adjusted Râ•›2, F-statistic, and sum of squared errors in table 14.10 compare to those for the pooled regression of table 14.4? Is this a surprise? Why or why not?

(b) Calculate the predicted value of earnings for a white male, aged 30, with a high school degree using the regression of table 14.10 and the pooled regression of table 14.4. How do these predictions compare?

(c) Calculate the predicted value of earnings for a white male, aged 30, with a college degree using the regression of table 14.10 and the pooled regression of table 14.4. How do these predictions compare?

(d) Calculate the predicted value of earnings for a white male, aged 30, with a professional degree using the regression of table 14.10 and the pooled regression of table 14.4. How do these predictions compare?

(e) Explain why the comparisons of parts

b, c, and d would yield the same results if the predictions were for a woman, or for any of the racial or ethnic minorities, or for an individual of a different age.
(fâ•›) Based on the answers to parts

b, c,

d, and

e, does it matter which educational category we omit from our regression? Why or why not?

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TABLE 14.10 Pooled earnings regression, sample from section 7.6 Explanatory variable Slope t-statistic Intercept 19,798 13.51 Female -18,343 94.92 No schooling completed -59,165 54.19 Nursery school to 4th grade -58,150 47.54 5th or 6th grade -57,223 53.89 7th or 8th grade -56,604 49.77 9th grade -56,458 50.08 10th grade 11th grade -56,086 49.31 -55,520 50.53 12th grade, no diploma -53,566 51.83 High school graduate -50,311 52.30 Some college, but less than one year -45,268 45.13 One or more years of college, no degree -42,020 43.36 Associate degree -39,409 39.08 Bachelor's degree -25,137 26.05 Master's degree Professional degree Age -12,815 12.57 12,735 11.13 3,201.8 58.73 Age squared -36.369 56.21 Black -7,987.2 19.64 Hispanic -6,275.9 23.74 American Indian or Alaskan Native -8,579.8 10.19 Asian -7,776.9 24.40 Native Hawaiian, other Pacific Islander -3,472.3 2.33 R .2089 Adjusted R .2088 F-statistic 2,060.6 p-value for F-statistic